I feel that any mid-caliber cartridge (6mm to 8mm) capable of launching a mid-weight projectile 3 to 5 calibers in length at around 2,700 fps will do very well as an all-around cartridge. Of course, this includes all of the most popular rounds available: 243, 25-06, 270, 7X57, 280, 308, 30-06, 8X57. Looking at a list of most popular chamberings, my bet would be that a large majority of people prefer to shoot rifles in this range, and that they work well.
Outside either extreme of this class, you get rifles that are fully capable of doing the job, but that people either do not enjoy shooting or will not shoot as an all-around cartridge. Like the 220 Swift, 375 H&H, 458 WM, etc. Whether it's because of recoil, rifle weight, bullet construction, etc.
Most common calibers have ample energy to compensate for errors of bullet placement, range estimation, uphill/downhill, etc, but not so much extra energy that they kill at one end and maim at the other.